But there’s no way to skip HDMI right? I mean I’m not familiar with ML, but think whether some wiring can be spared. Don’t these cameras expose wifi of some sort?

IMHO even 800x600 is okay for most streaming needs. And particularly when sound quality is of primary importance.

600D doesn't have WiFi. You can stream via HDMI or USB. USB stream for cams not supporting UVC (in general every EOS before Digic X and even some of those) is limited to 576p. Don't get your hopes high subscribing to EOS Webcam Utility Pro. Canon says it is able to deliver 720p and 1080p but they are scaled up from 576p. And you need a dedicated mic. No audio support via USB or HDMI in early cams.